# ApCoCoA-1:Num.EigenValues

From ApCoCoAWiki

## Numerical.EigenValues

Eigenvalues of a matrix

### Syntax

$numerical.EigenValues(A:Matrix):List

### Description

This function returns a matrix, containing numerical approximation to A's eigenvalues.

Therefore the input matrix A has to be rectangular!

It is implemented in the ApCoCoA server, so you need a running server. It was not implemented in version 0.99.4 or previous. Also please keep in mind this method is based on blas/Lapack's eigenvalue solver and uses floating point arithmetic. This is not an exact, algebraic method! The output contains of a matrix B, where the number of rows contains one of A's eigenvalues. The first column contains the eigenvalue's real part, the second the imaginary.

#### Example

A:=Mat([[1,2,7,18],[2,4,9,12],[23,8,9,10],[7,5,3,2]]); Numerical.EigenValues(A); -- CoCoAServer: computing Cpu Time = 0.0049 ------------------------------- Mat([ [2038617447977453/70368744177664, 1593056728295919/4503599627370496, 0, 1717983664400761/562949953421312], [-3850002255576293/281474976710656, 1593056728295919/4503599627370496, 0, -1717983664400761/562949953421312] ]) -------------------------------

### See also

Numerical.EigenValuesAndVectors

Numerical.EigenValuesAndAllVectors